U.S. patent application number 14/090753 was filed with the patent office on 2014-07-10 for optimized orthonormal system and method for reducing dimensionality of hyperspectral images.
The applicant listed for this patent is Raytheon Company. Invention is credited to Bradley Flanders, Ian S. Robinson.
Application Number | 20140193078 14/090753 |
Document ID | / |
Family ID | 46062041 |
Filed Date | 2014-07-10 |
United States Patent
Application |
20140193078 |
Kind Code |
A1 |
Robinson; Ian S. ; et
al. |
July 10, 2014 |
OPTIMIZED ORTHONORMAL SYSTEM AND METHOD FOR REDUCING DIMENSIONALITY
OF HYPERSPECTRAL IMAGES
Abstract
A method for reducing dimensionality of hyperspectral images
includes receiving a hyperspectral image having a plurality of
pixels. The method may further include establishing an orthonormal
basis vector set comprising a plurality of mutually orthogonal
normalized members. Each of the mutually orthogonal normalized
members may be associated with one of the plurality of pixels of
the hyperspectral image. The method may further include decomposing
the hyperspectral image into a reduced dimensionality image,
utilizing calculations performed while establishing said
orthonormal basis vector set. A system configured to perform the
method may also be provided.
Inventors: |
Robinson; Ian S.; (Redondo
Beach, CA) ; Flanders; Bradley; (Whittier,
CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Raytheon Company |
Waltham |
MA |
US |
|
|
Family ID: |
46062041 |
Appl. No.: |
14/090753 |
Filed: |
November 26, 2013 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
13085883 |
Apr 13, 2011 |
8675989 |
|
|
14090753 |
|
|
|
|
Current U.S.
Class: |
382/191 |
Current CPC
Class: |
G01J 2003/2836 20130101;
G01J 3/027 20130101; G06K 9/46 20130101; G01J 3/06 20130101; G06K
9/0063 20130101; G01J 3/0264 20130101; G01J 3/2823 20130101 |
Class at
Publication: |
382/191 |
International
Class: |
G06K 9/46 20060101
G06K009/46 |
Claims
1-12. (canceled)
13. A method of hyperspectral image dimension reduction,
comprising: receiving a hyperspectral image having a plurality of
pixels; iteratively establishing a basis vector (BV) set comprising
an initial basis vector and individual spectral vectors from the
plurality of pixels that have a residual magnitude over a threshold
value when a spectral vector of a current iteration is unmixed by
unconstrained unmixing with a prior iteration of the BV set; for
each of the plurality of pixels: reading a spectral vector from the
pixel; and decomposing, by unconstrained unmixing, the spectral
vector with the established BV set to provide a reduced dimension
vector for the pixel; and providing a dimension reduced image
comprising the reduced dimension vectors for each pixel.
14. The method of claim 13, wherein the residual vector is
orthogonal to a prior iteration of the BV set.
15. The method of claim 13, wherein said basis vector set comprises
at least one non-endmernber.
16. The method of claim 13, wherein said establishing the BV set is
configured to minimize error associated with each of the plurality
of pixels.
17. The method of claim 13, wherein the dimension reduction is
performed as a lossless process.
18. The method of claim 13, wherein the dimension reduced image
includes an alpha vector and a residual vector for each pixel.
19. The method of claim 13, wherein establishing a basis vector
(BV) set includes: selecting an initial pixel; reading the spectral
vector for the initial pixel, the spectral vector set assigned as
an initial basis vector (BV) of the set; and for each of the
remaining plurality of pixels: reading a spectral vector from the
pixel; unmixing the spectral vector with the BV set to determine a
residual vector; and in response to a magnitude of the residual
vector being greater than a threshold, adding the spectral vector
to the BV set.
20. The method of claim 19, wherein the BV set has a pre-determined
maximum number of members, and in response to an attempt to exceed
the maximum number, optimizing the set to maintain the maximum
number of spectral vectors.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a Divisional application of U.S. patent
application Ser. No. 13/085,883 filed on Apr. 13, 2011, which is
related to U.S. patent application Ser. No. 12/475,145, entitled
"System and Method for Reducing Dimensionality of Hyperspectral
Images," filed May 29, 2009, and is related to U.S. patent
application Ser. No. 11/856,588, entitled "Hyperspectral Image
Dimension Reduction System and Method," filed Sep. 17, 2007, the
disclosures of which are hereby incorporated by reference in their
entireties.
BACKGROUND
[0002] This disclosure relates to compression and dimensionality
reduction (DIMRED) of hyperspectral image data, based on an
optimized set of basis vectors. While compression reduces the size
of a data set, it typically results in a loss of access to
information content. On the other hand, DIMRED techniques provide
compression with the ability to extract information from the data
set in its reduced size. Thus, while all DIMRED techniques provide
compression, not all compression techniques allow for DIMRED.
[0003] Hyperspectral sensors can collect image data cross a
multitude of spectral bands through a combination of technology
associated with spectroscopy and remote imaging. Thus, such sensors
can capture sufficient information to derive a generally contiguous
spectrum for each pixel in an image. In addition to having a color
value, each pixel in the image additionally has a third dimension
for a vector providing distinct information for the pixel over a
large spectrum of wavelengths. This contiguous spectrum may be
analyzed to separate and evaluate differing wavelengths, which may
permit finer resolution and greater perception of information
contained in the image. From such data, hyperspectral imaging
systems may be able to characterize targets, materials, and changes
to an image, providing a detection granularity which may exceed the
actual resolution of pixels in the image and a change
identification capability that does not require pixel level
registration, which may provide benefits in a wide array of
practical applications.
[0004] Because each pixel carries information over a wide spectrum
of wavelengths, the size of a hyperspectral data set may often
quickly become unwieldy in terms of the size of data that is being
recorded by the hyperspectral sensor. As an example, hyperspectral
sensors are often located remotely on satellites or aircraft
capable of imaging areas in excess of 500 km.times.500 km per hour,
which may result in the hyperspectral sensors generating anywhere
from three to fifteen gigabits of data per second. Where the
hyperspectral data needs to be processed in near real time, the
large size of the data may introduce latency problems. In some
cases, it may be desirable to transmit the data to a remote
location for processing or other analysis, which again would make a
reduced data size desirable.
[0005] Although the transmission rate for hyperspectral images can
be increased using existing lossy and/or lossless compression
techniques, these techniques also suffer from various drawbacks.
For example, while lossy compression methods may be fine for casual
photographs or other human viewable images, wherein the data that
is removed may be beyond the eye's ability to resolve, applying
such lossy compression methods to a hyperspectral data set may
remove information that is valuable and desired for further
computer or mathematical processing. Such removal of data may
undermine the ability to characterize targets, materials, or
changes to scenes that are captured in hyperspectral images.
Lossless data compression would not remove such valuable
information, since lossless algorithms produce a new data set that
can subsequently be decompressed to extract the original data set.
Although general purpose lossless compression algorithms can
theoretically be used on any type of data, existing lossless
compression algorithms typically cannot achieve significant
compression on a different type data than that which the algorithms
were designed to compress. Thus, existing lossless compression
algorithms do not provide a suitable guaranteed compression factor
for hyperspectral images, and in certain cases, the decompressed
data set may even be larger than the original data set.
[0006] DIMRED techniques strike a balance between the loss of data
resulting from lossy compression, and the increased processing
requirements of lossless techniques. For example, the DIMRED
techniques may identify information that is of particular
importance, and segregate it such that it is not compressed, while
compressing the remaining information that is of less value. Thus,
the use of DIMRED on hyperspectral data sets allows for
transformation of the hyperspectral image into a more compact form,
with little to no loss of the most relevant information. At the
same time, it is advantageous for DIMRED techniques to facilitate
rapid processing of a reduced hyperspectral image data set.
Typically for DIMRED of hyperspectral images, a family of functions
or a set of vectors are found whose arithmetic combination can
represent all of the data in a three-dimensional (3D) data set.
Hyperspectral image data is generally discrete, so at each X/Y
location in a hyperspectral image the spectral data may form
elements of a vector. Depending on the nature of these vectors,
they may either be characterized as endmembers (EMs) or basis
vectors (BVs). While BVs span the data obtained from the image, and
form a mathematical basis for the data, EMs are pixels from an
imaged scene (or extrapolations of pixels in the scene), that
represent the spectra of a pure material found in the scene. In
some cases, EMs are derived such that they enclose or bound the
data set (as in a hypervolume or a simplex).
[0007] Among other things, it is advantageous to increase the speed
at which the dimensionality of hyperspectral images is reduced, and
to improve the identification of which data is to be compressed or
not.
SUMMARY
[0008] According to an embodiment, a method for reducing
dimensionality of hyperspectral images includes receiving, from a
sensor, a hyperspectral image having a plurality of pixels. The
method may further include, by using a processor, establishing an
orthonormal basis vector set comprising a plurality of mutually
orthogonal normalized members, each associated with one of the
plurality of pixels. The method may further include, by using the
processor, decomposing the hyperspectral image into a reduced
dimensionality image utilizing calculations performed while
establishing said orthonormal basis vector set.
[0009] According to another embodiment, a system for reducing
dimensionality of hyperspectral images includes one or more storage
devices, and one or more processors operatively coupled to the one
or more storage devices. The one or more processors may be
configured to receive, from the one or more storage devices, a
hyperspectral image having a plurality of pixels. The one or more
processors may be additionally configured to establish and store an
orthonormal basis vector set comprising a plurality of mutually
orthogonal normalized members, each associated with one of the
plurality of pixels. Furthermore, the one or more processors may be
configured to decompose the hyperspectral image into a reduced
dimensionality image utilizing calculations performed while
establishing said orthonormal basis vector set.
[0010] Other features of this disclosure and the inventive concept
described herein will be apparent to those skilled in the art based
on the following drawings and detailed description.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] FIG. 1 illustrates an exemplary system for reducing
dimensionality of one or more hyperspectral images, according to an
embodiment.
[0012] FIG. 2 illustrates an exemplary representation of one or
more hyperspectral images, according to an embodiment.
[0013] FIG. 3 illustrates an exemplary high level method for
reducing dimensionality of one or more hyperspectral images,
according to an embodiment.
[0014] FIG. 4 illustrates an exemplary detailed method for reducing
dimensionality of one or more hyperspectral images, according to an
embodiment.
[0015] FIG. 5 illustrates another exemplary detailed method for
reducing dimensionality of one or more hyperspectral images,
according to an embodiment.
[0016] FIG. 6 illustrates another exemplary detailed method for
reducing dimensionality of one or more hyperspectral images,
according to an embodiment.
DETAILED DESCRIPTION
[0017] Depicted in FIG. 1 is an embodiment of DIMRED system 100
that is configured to reduce a dimensionality of hyperspectral
images. As shown, hyperspectral imaging system 102 may incorporate
DIMRED system 100, and may be coupled to or otherwise contained
within remote imaging system 104. Remote imaging system 104 may be
of any suitable construction or configuration, including but not
limited to comprising a satellite, an aerial surveillance system,
or any other system that can capture hyperspectral images. In an
embodiment, remote imaging system 104 may be configured to capture
one or more images of a particular scene 106 corresponding to a
geographical area.
[0018] In an embodiment, remote imaging system 104 may be
configured to use hyperspectral imaging system 102 to capture a
hyperspectral image of scene 106. Scene 106 may correspond to the
geographical area, for example, where remote imaging system 104 is
located on a space-based satellite, an airplane, or other elevated
imaging system. In an embodiment, hyperspectral imaging system 102
may include one or more scan mirrors 110, or may include other
optics arranged to receive light 108 from one or more ground
resolution cells. In an embodiment, scan mirrors 110 or the other
optics may then direct light 108 through dispersing element 112,
which may be arranged to separate light 108 into various different
wavelengths (i.e. a spectra). After being separated into the
various different wavelengths, light 108 may then be directed to
one or more imaging optics 114, which may focus the various
wavelengths onto detector array 116. As such, detector array 116
may capture hyperspectral data across the spectrum of wavelengths,
thereby generating a data set corresponding to a hyperspectral
image of scene 106.
[0019] Following the generation of the data set corresponding to
the hyperspectral image of scene 106, DIMRED system 100 may process
the data set so as to reduce the dimensionality of the
hyperspectral image. In an embodiment, as described in greater
detail below, the degree to which the dimensionality of the image
is reduced and/or whether the dimensionality reduction is to be
classified as lossy or lossless may be determined by adjustable
features of DIMRED system 100. As such, after the dimensionality of
the hyperspectral image has been reduced, a data set corresponding
to the reduced hyperspectral image may be processed in various
ways. For example, in an embodiment, the reduced hyperspectral
image may be processed to characterize targets or materials in
scene 106, detect changes between various different hyperspectral
images captured for scene 106, or perform other analytics on the
reduced data set for the hyperspectral image.
[0020] In some embodiments, DIMRED system 100 may contain or
otherwise provide a front end interface for one or more local
processors associated with remote imaging system 104. In some such
embodiments, the one or more processors may be configured to
analyze the reduced data set for the hyperspectral image without
requiring the reduced data set to be decompressed or otherwise
processed to reconstruct an original (i.e., unreduced) data set for
the hyperspectral image. In some embodiments, DIMRED system 100 may
alternatively or additionally be configured to compress the
hyperspectral image, wherein the reduced data set can be
communicated rapidly within transmission 118 to remote station 120,
which may be a ground station or other remote location where the
data set can be further processed. For example, remote station 120
or other processing locations may analyze the reduced data set for
the hyperspectral image without further decompression, after
decompressing the reduced data set to produce the original data
set, or any appropriate combination thereof.
[0021] FIG. 2 provides an exemplary representation of hyperspectral
image 200, which may generally include a plurality of images
200i-n, which may be acquired in a substantially simultaneous
manner across various different wavelength (.lamda.) bands. As
shown in FIG. 2, hyperspectral image 200 may include a plurality of
pixels 202 arranged according to an x-y coordinate system, although
it will be apparent that alternate coordinate systems may be
employed in various circumstances. In an embodiment, each
respective pixel 202 may have spectral vector 204 associated
therewith, wherein spectral vector 204 may contain one or more
spectral measurements representing energy associated with the
respective pixel 202. For example, FIG. 2 further illustrates an
enlarged section 206 representing a particular row X' of pixels
202a-n from one of the plurality of images 200i-n, wherein each of
the various pixels 202a-n in the row X' may have a spectral vector
204a-n representing the energy associated with the respective pixel
202.
[0022] In an embodiment, hyperspectral image 200 may include BV set
208 having one or more BVs 210, which may be associated with one or
more parameters for controlling error levels, fidelity, or other
parameters of individual spectra in hyperspectral image 200. For
example, a maximum error may be defined for each of pixels 200,
wherein BV set 208 may include a minimum number of BVs 210 derived
as a function of the maximum error defined for each respective
pixel 200. In an embodiment, BV set 208 may be derived without a
priori knowledge of imaged scene 106, wherein BVs 210 may instead
be derived to span background materials, statistically sparse
targets, or other relevant objects within scene 106. As an example,
DIMRED system 100 may be configured to derive BVs 210 in a manner
that represents endmembers for pixel spectra associated with unique
objects or other targets in scene 106. In some embodiments, DIMRED
system 100 may be configured such that analysts or other users may
alternatively or additionally select one or more pixel spectra to
be added to BV set 208, or one or more pixel spectra collected
and/or measured a priori can be added to BV set 208. Basis vectors
210 provided in BV set 208 may then provide a reduced
dimensionality data set for hyperspectral image 200 of scene 106,
which can be processed by any known mechanism for processing
hyperspectral data in the form of one or more basis vectors.
[0023] FIG. 3 depicts an embodiment of a method 300 for reducing
dimensionality of one or more hyperspectral images. It will be
understood and appreciated that some elements of method 300 need
not be performed in the particular order illustrated in FIG. 3 and
described in further detail herein, but rather may be performed in
any suitable order that can result in a reduced dimensionality data
set from a data set corresponding to an incoming hyperspectral
image. Furthermore, some steps of method 300 may be optional in
some embodiments.
[0024] In an embodiment, method 300 may generally include any
suitable sequence in which a data set for a hyperspectral image is
received (operation 310). Although the hyperspectral image received
at 310 may be similar to hyperspectral image 200 described above,
and may similarly be received by remote imaging system 104 also
described above, other configurations of the data set and
hyperspectral imaging systems for receiving it are also possible.
Once the hyperspectral image is received at 310, it may then be
processed to establish a BV set for the hyperspectral image
(operation 320).
[0025] As described in greater detail below, establishing the BV
set at 320 may first include finding an initial BV, which may also
be characterized as a seed BV, and may be utilized to establish the
remainder of the BV set for the hyperspectral image. In some
embodiments, the initial BV found at 320 may comprise a normalized
pixel/vector selected at random from the hyperspectral image. In
other embodiments, the initial BV may comprise a normalized pixel
that is pre-determined on the hyperspectral image (such as, for
example, the upper left pixel, the center-most pixel, or so on). In
an embodiment, the initial BV may comprise a normalized vector that
is calculated from two or more of the pixels in the hyperspectral
image. For example, the calculated normalized vector may be
averaged from across all pixels in the hyperspectral image. As
another example, in some embodiments, the calculated normalized
vector may exclude outliers (i.e. statistical anomalies). Other
mechanisms for selecting or calculating the initial BV may be
performed by any suitable process or input, and the examples
described herein are not intended to be limiting in any way.
[0026] As described in greater detail below, establishing the
remainder of the BV set may utilize the initial BV in an iterative
process, by which each BV of the BV set is calculated by the
previous BVs of the BV set. For example, in an extremely simplified
example where there are only five pixels in the hyperspectral
image, if the first pixel is normalized as the initial BV, BV(1),
then BV(2) may be calculated from BV(1), BV(3) may be calculated
from both BV(1) and BV(2), BV(4) may be calculated from BV(1),
BV(2), and BV(3), and BV(5) may be calculated from BV(1), BV(2),
BV(3), and BV(4). How each BV may be calculated from the previous
BVs in some embodiments is described below.
[0027] As shown, in some embodiments, developing the BV set at 320
may include generating dimension reduced data that is associated
with the hyperspectral image. In an embodiment, the dimension
reduced data may be considered a dimension reduced image. In some
embodiments, reducing the dimensionality of the hyperspectral image
may include decomposing (e.g., unmixing) each pixel in the
hyperspectral image to generate the reduced dimensionality data
set. Unmixing, as used herein without further modifiers, is
understood to generically refer to the broad concept of
unconstrained unmixing. In some embodiments, the dimension reduced
data may then be output at 330, and may be utilized for any
suitable purpose, including undergoing further processing, being
transmitted, stored, viewed, analyzed, or so on. In some
embodiments, the BV set may be output either alongside or as part
of the dimension reduced data. As is described in greater detail
below, in some embodiments assembling the dimensionally reduced
data may comprise utilizing stored results from calculations that
were performed in establishing the BV set.
[0028] Turning to FIG. 4, additional details of an embodiment of
method 300 for reducing dimensionality of a hyperspectral image may
be appreciated. As above, method 300 first comprises receiving a
hyperspectral image at 310. The hyperspectral image may be of any
suitable type or configuration, and generally will comprise raw
data in the form of a planar spatial dimensions (i.e. in an x-y
coordinate system), and spectral data on a Z axis. Additional
dimensions to the hyperspectral image are also possible, such that
spectral vectors are recorded therein. Further as above, receiving
the hyperspectral image at 310 may be by any suitable mechanism,
including but not limited to reading out and accumulating the raw
data from a hyperspectral imager, receiving transmitted data that
was previously recorded, or accessing stored raw data from a
storage device. In some embodiments, the hyperspectral image may
previously be partially compressed or otherwise reduced in
dimensionality, by which method 300 may attempt to further reduce
the dimensionality.
[0029] Additionally, FIG. 4 illustrates an expansion of an
embodiment of developing the BV set at 320. In the illustrated
embodiment, developing the BV set at 320 may include determining an
initial BV at 410, which may be used to further develop the BV set,
as described below. Determining an initial BV may be accomplished
by any suitable process. In some embodiments, the initial BV may be
user-supplied. In other embodiments, the initial BV may be read
from the hyperspectral image. In still other embodiments, the
initial BV may be calculated from the hyperspectral image. As shown
at 420, in some embodiments, the initial BV may be determined from
either a single pixel, or calculated from multiple pixels of the
hyperspectral image. Where a single pixel is being utilized to
determine the initial BV, the pixel may be selected at 430. The
selected pixel may be any pixel from the hyperspectral image. For
example, in some embodiments it may simply be the first spatial
pixel (i.e. the upper left pixel of the image), or may be chosen
from the spatial center of the image. In other embodiments, the
pixel used for the initial BV may be randomly selected. In some
embodiments, certain outliers, such as statistical anomalies in the
image, may be discounted when selecting the pixel. In an
embodiment, a pixel having a median spectra may be selected. Once a
pixel is selected, its spectral vector may be normalized at 440, to
create a vector of unity length, which may be utilized as the
initial BV.
[0030] In embodiments where multiple pixels are utilized to create
the initial BV at 420, method 300 may include selecting the
contributory pixels at 450. As above, in some embodiments the
contributory pixels may be selected to discount outliers or other
statistical anomalies. In some embodiments pixels at the edge of
the hyperspectral image may be ignored. Although any number of
calculations may be applied to the selected contributory pixels, in
the illustrated embodiment the contributory pixels are averaged at
460, so that the initial BV will be an average representation from
the scene. The averaged spectral vector calculated from 460 may
then be normalized at 470, to create a calculated vector of unity
length, which may then be utilized as a calculated initial BV.
[0031] After the initial BV is determined at 410, it may then be
added to a BV set at 480. As its name implies, the initial BV may
originally be the sole BV in the BV set. The current BV of the BV
set (i.e. the most recent BV added to the set) may then be
iteratively computed with each pixel to further develop the BV set.
As such, the spectral vector of a first pixel is read at 490. If
the current BV is the initial BV, determined at 500, then method
300 continues at 510 by computing the dot product between the
initial BV of the BV set and the pixel P. As discussed in greater
detail below, in an embodiment the dot product may also be stored
for future reference. In an embodiment, method 300 may continue by
assembling the dimensionally reduced data at 515. In an embodiment,
assembling the dimensionally reduced data at 515 may comprise
associating the dot product computed as part of a reduced dimension
spectral vector for the pixel P. In an embodiment, storing the dot
product at 510 may be directly into the reduced dimension spectral
vector, such that the storing is a part of assembling the dimension
reduced data at 515. As such, in an embodiment assembling the
dimension reduced data may be an incremental or iterative assembly.
As shown in the illustrated embodiment, method 300 may continue by
computing and storing the residual vector for the pixel P at 520.
In an embodiment, computing the residual vector at 520 comprises
multiplying the dot product calculated in 510 with the current BV
of the BV set, and subtracting the resulting quantity from the
spectral vector of the pixel read at 490. In an embodiment, this
calculation may result in the residual vector being orthogonal to
the initial BV. In addition to computation of the residual vector,
the residual magnitude for the pixel may also be computed and
stored at 530. In an embodiment, the computation of the residual
magnitude may be computed as the square root of the quantity of the
square of the pixel magnitude minus the square of the dot product.
In an embodiment the computation of the residual magnitude may also
be stored in a memory for future reference.
[0032] Following computation of the residual magnitude at 530,
method 300 may continue at 540 by ascertaining if there are
additional pixels in the hyperspectral image. If there are
additional pixels, method 300 may increment to the next pixel at
550, returning to 490 and continuing the calculations through the
pixels of the hyperspectral image. Although in some embodiments
pixels are incremented in an orderly fashion, the specific manner
for incrementing pixels may include any suitable technique (e.g.,
from left to right, from right to left, from top to bottom, from
bottom to top, randomly, etc.). If at 540 it is determined that
there are no additional pixels in the hyperspectral image, method
300 may continue at 560 by identifying the residual vector having
the largest residual magnitude. This may be accomplished, for
example, by ranking the residual magnitudes associated with each
pixel that were calculated at 530, and selecting the largest one
therefrom. As shown in the illustrated embodiment, the identified
residual vector may be the one having the largest residual
magnitude that is associated with a pixel that has not been
previously labeled as anomalous in a prior iteration, as described
in greater detail below. Once the residual vector with the largest
residual magnitude is identified, it is then normalized at 570.
Since the magnitude of the vector was previously computed at 530,
its magnitude would not need to be recomputed to normalize the
vector, but rather the elements of the vector would just be divided
by the previously computed residual magnitude. As previously
indicated, the residual vector would be orthogonal to the seed
vector. As such, by normalizing the orthogonal residual vector at
570, an orthonormal BV is established.
[0033] Method 300 may then continue at 580 by determining if the BV
set is to be further developed. The determination as to how to
further develop the BV set may be made by any appropriate measure.
For example, in various embodiments the BV set may have a
user-defined size that it will grow to. In an embodiment, the BV
set may continue to grow until a calculated stopping point is
reached. For example, in an embodiment the BV set will continue to
grow until the residual magnitude calculated at 530 is below a
selected threshold for each pixel. Other mechanisms for determining
the size of the BV set are also possible. If the determination at
580 is to continue to grow the BV set, method 300 may continue by
adding the orthonormal vector to the BV set at 480 as the new
current BV.
[0034] The process then would repeat with the new current BV, which
would be determined at 500 to not be the initial BV. As shown in
FIG. 4, for subsequent BVs, instead of computing and storing the
dot product between the initial BV and the pixel as was performed
at 510, the dot product between the current BV and the prior
residual vector for the pixel (which was calculated and stored for
the pixel at the prior iteration of 520) is calculated and stored
at 590. Again, the dot product may be used to further assemble the
dimension reduced data at 515, as described above, and may in some
embodiments be a part of the storing at 590. Although in some
embodiments the calculations for the new dot products would replace
those from the prior iteration, in other embodiments the
calculations are retained throughout the DIMRED operation. The new
dot product calculated at 590, which is based on the prior
iteration, and thus is iteratively related to the initial BV, is
then used when computing and storing the new residual vector for
the pixel at 520. The new dot product is also used when computing
and storing the new residual magnitude for the pixel at 530, which
for the subsequent iterations would again use the residual
magnitude which was previously computed. The computational
enhancement from reutilizing prior calculations in subsequent
iterations when establishing the BV set is clear.
[0035] As long as the BV set continues to grow, as determined at
580, the prior iteration's computations may be utilized to
determine the subsequent BVs of the BV set. Because each BV is
orthonormal to the seed vector, they are also mutually orthonormal
to each other. Eventually, as described above, it may be determined
that the BV set is complete. Method 300 would then continue at 600,
whereby the normalized residual vector having the largest residual
magnitude is added as the final BV of the BV set, completing the BV
set. In some embodiments, such as that shown in FIG. 4, method 300
may include as part of developing the BV set anomaly analysis,
which may determine a subset of pixels that are not to be included
in the computation of the BV set. In the illustrated embodiment, it
may be determined at 610 whether anomalies have previously been
analyzed when computing the BV set. Although in some embodiments
this will only be ascertained once, in other embodiments there may
be an iterative anomaly analysis, wherein the BV set is
continuously analyzed until certain conditions regarding anomalies
are met. If anomalies have not been accounted for, however, method
300 may continue at 620, wherein the anomalies are detected and
ranked.
[0036] In some embodiments, detecting and ranking the anomalies at
620 may utilize the first complete BV set established at 600. In
other embodiments, detecting and ranking anomalies at 620 may
utilize DIMRED data computed for the current BV set, such that
method 300 may continue to generate dimension reduced data at 320
with the completed BV set from 600, before looping back, as
described below. In an embodiment, anomalies may cause the first
pass of the hyperspectral image to create the initial basis vector
set with more basis vectors than desired (e.g., because the basis
vectors were assigned to pixels that were atypical of the scene,
generally corresponding to targets or sensor artifacts). Thus, in
one implementation, detecting and ranking anomalies at 620 may
include decomposing each pixel in the reduced dimensionality data
set with the initial basis vectors derived for the reduced
dimensionality data set to derive a residual vector and a fitting
coefficient with respect to each of the basis vectors in the
initial basis vector set. In some embodiments, the decomposing may
comprise unmixing. As such, pixels may be identified in the reduced
dimensionality data set that may qualify as anomalies, and such
potentially anomalous pixels may be ranked according to the
magnitudes of the residual vectors and/or the fitting coefficients
for the potentially anomalous pixels. Based on the magnitude of the
residual vectors and/or the fitting coefficients for the pixels
that are ranked, some of which may have already been computed and
stored when establishing the BV set, a predetermined percentage or
ratio of the pixels that are more than a particular threshold from
zero may then be considered a potential "anomaly." Alternatively,
every pixel that varies from zero by more than the threshold may be
a potential anomaly. In some embodiments, method 300 may apply
other algorithms for anomaly detection, including but not limited
to the conventional "R-X algorithm," which may make use of the
calculations and/or data generated in method 300 or associated with
the hyperspectral image.
[0037] After detecting and ranking the anomalies at 620, method 300
may continue at 630 by labeling a threshold number of pixels as
anomalous, and characterizing the remaining (non-anomalous) pixels
in the scene as "common." In an embodiment, such labeling is only
for the purposes of establishing the optimized BV set, whereby all
pixels in the hyperspectral image will ultimately be reduced. In an
embodiment, in addition to the anomalous pixels, pixels that appear
in a predetermined neighborhood of the anomalous pixels, or are
otherwise associated with the anomalous pixels, may also be
considered anomalous. For example, the neighborhood of the
anomalous pixels may be defined to include any pixels within a
particular window surrounding the anomalous pixels (e.g., the
window may include the eight pixels immediately adjacent to any
particular anomalous pixel, although the window may vary in size
depending on the particular application). In other embodiments, the
neighborhood of the anomalous pixels may be defined to include a
number of pixels in the same row and/or the same column as the
anomalous pixels. In an embodiment, the entire row or the entire
column of pixels associated with an anomalous pixel may also be
considered anomalous. As such, setting aside the anomalous pixels
and any pixels in the neighborhood of the anomalous pixels may
result in less pixels being eligible to be used in establishing the
BV set. In some embodiments, worst case error or mean-squared error
may be measured on all of the pixels of the hyperspectral image, or
a subset thereof (i.e. the non-anomalous pixels), to determine
inclusion or exclusion of the pixels in establishing the BV set.
For example, in an embodiment an adaptive error threshold may be
applied, such that anomalous pixels having a larger residual
magnitude than the worst case error on the compressed pixel may be
set aside as "raw" pixels. As such, in various embodiments the
DIMRED data may include both raw pixels and dimensionally reduced
pixels for some or all of the hyperspectral imaged.
[0038] As shown in the embodiment of FIG. 4, once the anomalous
pixels are labeled as such, a new BV set may be computed by
utilizing a reduced hyperspectral image that omits the anomalies.
In the illustrated embodiment the new hyperspectral dataset is
treated as the received hyperspectral image at 310, such that an
initial BV is again established at 410. Such a renewed calculation
may be useful, as the randomly or pre-determined pixel may itself
have been anomalous during the first determination of the BV set.
Even where the previous initial BV was averaged over the pixels,
the inclusion of anomalous pixels in computing the initial BV may
itself have skewed results. In other embodiments, however, a seed
BV may have been previously known as non-anomalous, and thus the
initial BV might be retained from the previous calculation of the
BV set. In some embodiments, the second BV set may or may not
include a maximum number of members for the new BV set. However, if
a particular compression ratio is required for the reduced data set
to be produced in the second pass, a maximum number of members may
be defined for the new BV set so as to insure the relevant
compression ratio.
[0039] As such, the number of BVs in the reduced data set produced
in the second pass may have a substantially reduced number of
members after the anomalous pixels in the scene have been labeled
such (i.e., as compared to the initial set of basis vectors).
Furthermore, the reduced data set produced in the second pass may
suitably span a complex scene even with the substantially reduced
number of basis vectors. In particular, the anomalous pixels in the
scene may generally correspond to the most unique or unusual
aspects of the scene, whereby removing the anomalies may preserve
those aspects of the scene that are most likely to be relevant to
detecting targets in the scene or detecting changes from prior
versions of the scene. In addition, reducing the dimensionality of
the hyperspectral image by performing multiple passes when
generating the BV set, with the anomalous pixels not used to
generate BVs in the second pass, may provide a larger compression
or reduction ratio for the final reduced data set because the
second pass dimensionality reduction pass might only be applied to
the most typical or otherwise common aspects of the scene. Thus,
preserving the full dimensionality of the anomalous pixels and the
pixels in the neighborhood of the anomalous pixels may provide the
maximum information content that may be relevant to analyzing the
reduced data set for the scene.
[0040] In some embodiments, the calculations that were utilized
when establishing the prior BV set (i.e. the first BV set, when the
anomalies of the BV set determined at 610 is only analyzed once)
may be further utilized by retrieving them from where they were
previously stored. Because the BV set is iteratively grown, the
calculations that are stored may in some embodiments lose their
computational usefulness once a first anomalous pixel is passed
over. For example, if the first ten pixels are non-anomalous, but
the eleventh pixel was anomalous, then the computations (i.e. the
dot product computation at 510/590, the residual vector computation
at 520, and the residual magnitude computation at 530) completed
for the first ten pixels may be reutilized, provided that the
initial BV is maintained.
[0041] As indicated above, in an embodiment the determination at
610 may be recursive. In such an embodiment the common pixels may
be again analyzed at 620 to detect whether any further anomalies
are present in the reduced data set produced in the second pass,
wherein the reduced data set produced for the common pixels may be
processed again in a similar manner as described above. If,
however, it is determined at 610 that the anomalies have been
accounted for, then method 300 may continue at 640, where the
optimized BV set is established, generally without the influence of
anomalous pixels. As shown, method 300 may then continue to 330,
whereby the dimension reduced data (i.e. the dimension reduced
hyperspectral image) may be output. In an embodiment, such as that
shown, the dimension reduced data may further be output with the
optimized BV set established at 640.
[0042] In an embodiment, the dimensionally reduced hyperspectral
image incrementally assembled at 515 and output at 330 may comprise
the same X/Y dimensions as the hyperspectral image received at 310,
however contains reduced spectral data instead of unreduced
spectral data. In an embodiment, the reduced dimension spectral
data for each X/Y pixel comprises the dot products stored at 510
and 590. As also shown, in some embodiments the optimized BV set
established at 640 may additionally be output at 330, either
alongside or as a part of the dimensionally reduced data. In some
embodiments, the reduced spectral data may be constructed as a
linear combination of the BVs of the BV set. In some embodiments,
the coefficient for each BV in this linear combination is the
previously obtained dot product. While in some embodiments, the dot
product may become an element of the reduced dimensionality vector
at each X/Y location (i.e. for each pixel) during incremental
assembly of the dimensionally reduced data at 515, in other
embodiments the results of the calculations may be stored
separately for subsequent assembly into the dimension reduced
image. In an embodiment, the reduced dimensionality vector at each
X/Y location is the set of dot product results for each BV in the
BV set, such that the spectrum of the pixel can be constructed by a
linear combination of the BV with the dot product results as
coefficients. In some embodiments those pixels labeled as anomalies
(i.e. as described above) might not be included in the reduced
dimensionality data. In other embodiments the spectral data
associated with the anomalous pixels may be segregated and
additionally output at 330, including as a separate data set. In an
embodiment, the X/Y location of each pixel may be encoded in the
two separate lists of reduced dimensionality pixels: i.e. with
coefficients for each BV, and with the anomalous pixels, with
intensities in each spectral band. In an embodiment, the DIMRED
data that is output at 330 may comprise a three dimensional data
set, represented as a reduced dimensionality hypercube
corresponding to the hyperspectral image received at 310.
[0043] Turning to FIG. 5, it may be appreciated that in some
embodiments accounting for anomalies may occur during the
identification of which pixels are used to establish the BV set.
For example, the illustrated embodiment of method 300' shares
numerous characteristics with that of method 300 described above,
however does not include anomaly detection following establishment
of a BV set. Instead, after calculation of the residual magnitudes
530 for a given BV, when the residual vector having the largest
residual magnitude is identified at 560 (which, as above, may be
specifically for pixels not previously labeled as anomalous), it is
tested at 700 to see if it passes a spatial-spectral normality
test. In an embodiment the spatial spectral normality test may be a
multi-part test that may determine various levels of deviance for
the tested pixel. For example, in an embodiment the spatial
spectral normality test may include a spectral artifact test,
wherein the pixel associated with the largest residual magnitude is
tested for positive and/or negative spikes that are greater than a
given threshold. In some embodiments, the threshold may be
user-defined, while in other embodiments it may be calculated based
on the hyperspectral image. As an example, each spectral element
may be tested against the mean and the standard deviation of all
spectral elements. If the spectral element exceeds the threshold,
the element may be characterized as an artifact. If the spectral
element is within the spectral test's threshold, then a spatial
test may be applied. In an embodiment, the spatial test may compare
the residual magnitude of the pixel to a predefined neighborhood
around the element, to see if the residual magnitude is more than a
factor above the average of the neighborhood. In another
embodiment, a standard deviation of the neighborhood may be
calculated, and the spatial test may determine whether the residual
magnitude of the selected pixel is more than a number of standard
deviations (i.e. 3.sigma.) above the standard deviation of the
neighborhood). As before, where the residual magnitudes have
already been computed and stored across the hyperspectral image,
the magnitudes may simply be loaded and compared, instead of being
recalculated. In some embodiments, the defined neighborhood may be
user-selectable. In a non-limiting example, the spatial
neighborhood may be a 16.times.16 region around the selected pixel.
In other embodiments, instead of testing a local neighborhood, the
entire scene may be analyzed in the spatial test. In some
embodiments, if the pixel fails the spectral test, it may be
characterized as an anomaly.
[0044] If the selected pixel fails the spatial spectral normality
test at 700, it may be rejected as a potential BV. In some
embodiments, such as that shown, the selected pixel may be labeled
as rejected at 705, so as to prevent the pixel or associated pixels
from being tried again as a BV in a subsequent iteration. In some
embodiments, groups of associated pixels may be simultaneously
labeled as rejected at 705 to prevent usage as BVs. Instead, method
300' may proceed to 710, wherein the residual vector having the
next largest residual magnitude is selected, and tested by the
spatial spectral normality test at 700 (again, in some embodiments
excluding those for pixels previously labeled as anomalous). In an
embodiment, once a residual vector passes the spatial spectral
normality test at 700, method 300' may proceed to 720, whereby the
vector is normalized to be established as the subsequent BV. Method
300' may then continue at 580, as described above, by determining
if the BV set is to continue growing. If it is, method 300' would
return to 480, by adding the new BV to the BV set, and utilizing it
to further develop the BV set. If the BV set is determined as
complete, then method 300' continues to 600, where the BV set is
considered complete. As shown, in some embodiments the application
of the spatial spectral normality test at 700 may make redundant
any need for optimizing the BV set by detecting and ranking
anomalies at 620, as described above. Instead, in such embodiments,
the completed BV set at 600 may be established as already
optimized, and method 300' may continue by outputting the DIMRED
data at 330, as described above.
[0045] Although in some embodiments the DIMRED data may be
subsequently stored in a memory arrangement for future analysis, in
an embodiment such as that shown in FIG. 5, the final output at 330
may subsequently be tested for one or more known targets at 340. In
particular, the DIMRED data may generally include a reduced data
set for all pixels in the hyperspectral image and an unreduced data
set for the anomalous pixels, i.e., if the final reduced data set
is to be tested for known targets, the copies of the anomalous
pixels may remain unreduced to ensure that the maximum information
content is preserved for analysis, while the anomalous pixels in
the reduced data set may be accessed for applications simply
requiring capturing and storing a suitable data set for the scene.
In various embodiments, testing the hyperspectral image for known
targets may include testing the unreduced data set and/or the
reduced data set for known targets. In an embodiment, the known
target might be dimensionally reduced utilizing the BV set that
reduced the hyperspectral image, for equivalent spectral
dimensionality comparison. For example, in an embodiment reducing
the dimensionality of the target spectral vector may comprise
computing the dot product of target vector with each BV in the BV
set, such that the resulting dot product coefficients form a DIMRED
target vector. In an embodiment, the dimension reduced target
vector may then be compared with the DIMRED vectors across some or
all of the pixels of the dimension reduced data, to determine if
the target (or a spectral vector within a threshold amount of the
target) is present within that pixel. Such testing may be with
known spectra corresponding to known targets, and which may be
stored in a spectral signature database. For example, certain
materials or targets may be known to have particular spectral
characteristics, which may provide known signal waveforms that may
be used to detect such known materials or targets within a
particular pixel.
[0046] It may be appreciated that the dimensionally reduced
spectral data may in some embodiments be reconstituted back into
data that at least approximates the original spectral data. For
example, in an embodiment by multiplying each element of the
dimensionally reduced vector (i.e. the dot products) by the
associated BV that was additionally output at 330, then a number of
new vectors may be formed equal to the dimensionality of the
reduced dimension spectral data. By summing the new vectors, a
vector having the dimensionality of the original hyperspectral
vector at that pixel is formed, which at least approximates the
original hyperspectral vector.
[0047] Depicted in FIG. 6 is another embodiment of a DIMRED method,
specifically method of hyperspectral image dimension reduction
1300. It is understood and appreciated that the method need not be
performed in the order herein described but rather is presented for
ease of discussion and illustration in accordance with at least one
embodiment.
[0048] Moreover, in at least one embodiment, a hyperspectral image
is provided, block 1302. A BV set is developed with respect to the
hyperspectral image, block 1304. Then, with the BV set established,
each pixel is decomposed with the BV set to provide a plurality of
alpha vectors, block 1306. These alpha vectors are provided as the
reduced data set of the output scene, block 1308.
[0049] More specifically, as shown in FIG. 6, in at least one
embodiment the process of developing the BV set commences with
analysis of whether a seed basis vector has been provided, decision
1500. Stated simply, the basis vector set provides a collection of
spectral vectors by which the spectral vectors of all pixels within
the hyperspectral image are evaluated. Whereas in at least one
embodiment, the evaluation and comparison is based entirely upon
data already present in the hyperspectral image itself, in at least
one embodiment at least one basis vector is provided by an operator
or is read from a default file. Such a basis vector may, for
example, correspond to the spectral vector of a particular material
known to exist or expected not to exist, within the geographic area
from which the hyperspectral image was formed.
[0050] Where one or more seed vectors are provided as initial basis
vectors, the seed basis vector(s) is received and added to the
basis vector set, block 1502. To develop the reset of the BV set,
an initial pixel (P) is selected, block 1504. Generally, and in at
least one embodiment, the initial pixel is selected to be the first
pixel in the top left or bottom left corner, the pixels to be
compared in an incremental step pattern across each row X.
[0051] Where a seed vector is not provided, decision 1500, an
initial pixel is immediately selected, block 1506. The spectral
vector for this initial pixel is then read by the spectrum reader
and this initial spectral vector is used as the initial basis
vector for the further development of the BV set, block 1508. In at
least one embodiment, the selection of the initial pixel to
determine the initial basis vector is a random selection. In at
least one alternative embodiment, the initial pixel is selected to
be either the top left or bottom left corner pixel.
[0052] Moreover, if a seed basis vector(s) is provided then it is
treated as if it was the determined basis vector from an initial
pixel and the process immediately commences with unmixing and
testing as discussed below. If a seed basis vector is not provided,
then a pixel is selected and its spectral vector is adopted as the
initial basis vector, and then the process commences with unmixing
and testing as set forth below.
[0053] With an initial basis vector so determined, the process
increments to select the next pixel (P), block 1510. Generally, and
in at least one embodiment, it is understood and appreciated that
the pixels will be incremented through in a left to right iteration
for each row X.
[0054] The process now continues with the reading of the spectral
vector of pixel P, block 1512. The spectral vector of the selected
pixel is then decomposed with the members of the developing BV set.
In at least one embodiment the decomposition is performed by
unmixing the spectral vector with the members of the BV set.
[0055] Generally stated, unmixing is understood and appreciated to
be, in essence, an algebraic approach to decomposing the spectral
vector into its component parts. For example, a spectral vector
from a given pixel may comprise the spectrum elements indicative of
grass, aluminum and sand, and thus be a composite spectral vector.
When this vector is unmixed with vectors representative of aluminum
and sand, the spectral vector of grass will be revealed. The
unmixing process provides alpha coefficients representative of the
abundance of the basis vectors and will provide a residual vector.
The vector that is unmixed is an algebraic combination of the basis
vectors, weighted in some fashion by the alpha coefficients plus
the residual vector.
[0056] In at least one embodiment, the magnitude of the residual
vector is then determined, and is understood and appreciated to be
derived from the square root of the dot product of the residual
vector with itself, otherwise known as Euclidean distance provided
by the equation:
.parallel.x.parallel.:= {square root over (x.sub.1.sup.2+ . . .
+x.sub.n.sup.2)}.
where x=[x.sub.1,x.sub.2, . . . x.sub.n].
[0057] The magnitude of the residual vector is then evaluated with
a threshold value, decision 1516. In at least one embodiment the
threshold value is provided by an operator. The threshold value may
also be a pre-determined value that is hard coded into the method.
If the magnitude is over the threshold, decision 1516, the spectral
vector is added to the BV set, block 1518. In some embodiments,
there may be a pre-determined maximum number of members of the BV
set. When the total number of members is below this pre-determined
maximum there is of course no issue and the new spectral vector is
simply added to the BV set, decision 1520.
[0058] If, however, the maximum number of members has been reached,
the members of the BV set are optimized, block 1522. Various
optimization methods may be employed and in general the type of
optimization strategy adopted is determined by an operator. These
methods may include, but are not limited to, optimization to
selection of the maximum spectral vectors (e.g., the spectral
vectors having the greatest magnitudes), optimization to select the
greatest range between the spectral vectors, optimization to select
the spectral vectors closest to a spectral vector mean,
optimization to select the spectral vectors closest to a spectral
median.
[0059] In at least one embodiment, the residual magnitude is stored
when a basis vector is added to the BV set. When the maximum number
for the BV set is reached, the magnitude of a new residual must be
larger than the smallest residual computed from the existing
members of the BV set. If it is not, the new basis vector is not
added. If it is, then the new basis vector is added and the basis
vector that previously had the smallest residual is removed.
[0060] As indicated above, in at least one embodiment the user is
permitted to provide seed basis vectors. In at least one such
embodiment where the user has also set a maximum number for the BV
set, the seed basis vector(s) are treated as special and maintained
as core elements of the BV set. In one embodiment, this is achieved
by tagging the seed vectors such that they are not considered in
the elimination evaluation process. Moreover, in at least one
embodiment the maximum number of BV set members does not include
the seed basis vector(s). In an alternative embodiment, the maximum
number of BV set members may indeed include the seed basis
vector(s), but they are simply not included in the evaluation for
removal process. As such, key factors that are indicated by the
seed vector(s) are maintained within the BV set.
[0061] Having resolved the question of whether to add the residual
vector to the BV set, and whether to optimize the BV set, the
method continues to select the next pixel, decision 1524. If indeed
more pixels remain then the method will incrument to the next
pixel, block 1526. It should be understood and appreciated that,
although the incremental process is intended to be orderly, the
type of incrementing--left to right, right to left, top to bottom,
bottom to top, or random--is largely immaterial. The key element is
that each pixel of the hyperspectral image is being evaluated so as
to determine an appropriate set of basis vectors that are, in at
least one embodiment, inherently tied to hyperspectral image
itself
[0062] With the BV set so established, the method now continues
with the generation of the alpha vectors, block 1306. As in the
development of the BV set, the generation of the alpha vectors
begins with the selection of an initial pixel, block 1528. The
spectral vector is then read from the selected pixel, block 1530.
The spectral vector is then decomposed with the BV set, block 1532.
In at least one embodiment the decomposition is performed as
unmixing, as discussed above. It is to be realized that for each
member of the BV set there will be a corresponding value, an
unmixing coefficient. There will also be a residual vector.
[0063] For the given pixel, the unmixing coefficients represent an
alpha vector for the given pixel. It is further understood and
appreciated that the relative magnitude of dimension reduction is
approximately the difference between the number of elements in a
spectral vector originally present in the hyperspectral image and
the number of members in the applied BV set. For example, if there
were originally one-hundred spectral bands present in the
hyperspectral image, and twenty basis vectors in the BV set, the
dimension reduction represented by the alpha vectors would be about
eighty or a factor of five.
[0064] The process is continued for each pixel, as indicated by the
query to determine the presence of more pixels, decision 1536, and
the increment to the next pixel, block 1538 and the return to read
the spectral vector for the selected pixel, block 1530. Moreover,
all of the pixels in the hyperspectral image scene are unmixed with
the BV set so as to provide vectors having g coefficients
(corresponding to the number of members in the BV set) and a
residual vector for each X-Y location.
[0065] When the generation of alpha vectors has been accomplished
for all pixels of the hyperspectral image, the resulting set of
alpha vectors is provided as the output scene, namely a
dimensionally reduced hypercube. Because of the application of the
BV set, which is derived from the spectral vectors of each pixel,
to each pixel, the resulting information of each alpha vector has
approximately the same information content as the original pixel.
More specifically, the reduced alpha vector is still representative
of the composite spectral frequencies present in the pixel, such a
combination of grass, sand and metal as present in the original
spectral vectors is still represented in the alpha vector.
Furthermore, and quite advantageously, the dimensionally reduced
image provided by the alpha pixels is suitable for processing
without regeneration of the original image. Further, the maximum
loss of information on any pixel is minimized compared to any other
dimensionality reduction process. This is crucial when the image is
processed for subtle changes, the presence of small targets or
anomalies.
[0066] Decompression of the output image can be accomplished with
the use of the BV set. As such, in at least one embodiment the BV
set is provided as output with the dimension reduced image. The
residual vectors, if left untreated are understood to be of the
same size as the original data set. Calculating the magnitude for
each residual vector greatly reduces the volume of the data once
again.
[0067] Indeed, in at least one embodiment the magnitude of each
residual vector is also determined and provided as output in
addition to dimensionally reduced image represented by the alpha
vectors. Moreover, it is understood and appreciated that in varying
embodiments, the method 1300 may provide: the alpha vectors, the
magnitude of the residual vectors, the BV set, and combinations
thereof. As such, it is understood that the method is adaptable to
provide compression and dimension reduction options that range from
lossy to lossless.
[0068] Although in various embodiments the DIMRED methods described
herein may be implemented on any appropriate system or hardware,
such as DIMRED system 100 described above. In some embodiments,
DIMRED system 100 may be implemented on a computer system, which
may generally include typical computer components such as one or
more processors, memory modules, storage devices, input and output
devices, and so on. In an embodiment, DIMRED system 100 may be
maintained in an active memory of the computer system to enhance
speed and efficiency, and may further be coupled to a computer
network and utilize distributed resources associated with the
computer network. In various embodiments, DIMRED system 100 may
include one or more interfaces, one or more spectrum readers, and
one or more modules that may perform establishing the BV set,
decomposing the hyperspectral image, and evaluating the
hyperspectral image. In some embodiments, the one or more
interfaces may be configured to receive data corresponding to one
or more hyperspectral images, one or more BVs provided by a user,
an indication as to whether dimensionality reduction is to be
performed as a lossy or lossless operation, tolerance levels for
the amount of lost data in the dimensionality reduction, and/or
other information relating to the processing of hyperspectral
images. In an embodiment, the one or more interfaces may be
arranged to receive information directly from the user via an input
device associated with DIMRED system 100, or directly from a
component of DIMRED system 100 (such as from detector array 116
depicted in FIG. 1).
[0069] According to an embodiment, implementations of the various
systems and methods for reducing dimensionality of hyperspectral
images described herein may be made in hardware, firmware,
software, or various combinations thereof. For example, the systems
and methods for reducing dimensionality of hyperspectral images may
be implemented as computer executable instructions stored on a
non-transitory machine readable medium, which may be read and
executed using one or more physically separate or communicatively
coupled computer systems or other processing devices. The machine
readable medium may include various mechanisms for storing and/or
transmitting information in a manner readable by the computer
systems, the processing devices, or other machines. For example, a
machine readable storage medium may include read only memory,
random access memory, magnetic disk storage media, optical storage
media, flash memory devices, hard drives, and other media for
storing information, and a machine readable transmission media may
include signals such as carrier waves, infrared signals, digital
signals, and other media for transmitting information.
Additionally, although the above disclosure may describe methods,
firmware, software, routines, or instructions in terms of specific
exemplary aspects and implementations and performing certain
actions, it will be apparent that such descriptions are merely for
the sake of convenience and that such actions in fact result from
the computer systems, the processing devices, processors,
controllers, or other devices or machines executing the firmware,
software, routines, or instructions.
[0070] Furthermore, aspects and implementations may be described in
the above disclosure as including particular features, structures,
or characteristics, but it will be apparent that every aspect or
implementation may or may not necessarily include the particular
features, structures, or characteristics. Further, where particular
features, structures, or characteristics have been described in
connection with a specific aspect or implementation, it will be
understood that such features, structures, or characteristics may
be included with other aspects or implementations, whether or not
explicitly described. Thus, various changes and modifications may
be made to the preceding disclosure without departing from the
scope or spirit of the inventive concept, and the specification and
drawings should therefore be regarded as exemplary only, with the
scope of the invention determined solely by the appended
claims.
* * * * *